Abstract: The surfaces of J. Steiner, E. Kummer, E. Goursat et
al. are invariant against the interchange of the variables x, y and z
in their defining implicit functions They show the hexahedral symmetry
of a cube. This article describes a method to generalize them to the symmetries
of other Platonic bodies, i.e., to tetrahedral up to icosahedral symmetries and
displays the surfaces.
Keywords and phrases: implicit surfaces, surface of Steiner, surface of Kummer, surface of Goursat, Platonic bodies, central planes, polynomials of higher order, radial projection.
